Closed loop parameter identifiability and adaptive control of a linear stochastic system

Abstract

We show that if the parameters of a linear stochastic control system are identifiable using a persistently existing input then the same systems remains parameter identifiable if the system operates under closed loop in a certain way. We assume that the controller itself depends on the test value of the system parameters, and as usual the control signal is dithered. The estimation problem is formulated as the problem of minimizing an appropriate asymptotic cost function. It is shown that a suitable modification of the gradient of the cost function converts our problem into another problem for which Ljung's scheme can be applied. Thus the theorem provides a general method for the solution of the local adaptive control problem.